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In this paper, we shall give an affirmative answer tothe question raised by Kim and Tan [1] dealing with generalizedvector quasi-variational inequalities which generalize manyexistence results on (VVI) and (GVQVI) in the literature. Usingthe maximal element theorem, we derive two theorems on theexistence of weak solutions of (GVQVI), one theorem on theexistence of strong solution of (GVQVI), and one theorem on strongsolution in the 1-dimensional case.